Related papers: Fast binary embeddings with Gaussian circulant mat…
Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…
We consider the problem of embedding a subset of $\mathbb{R}^n$ into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high…
We propose a fast, distance-preserving, binary embedding algorithm to transform a high-dimensional dataset $\mathcal{T}\subseteq\mathbb{R}^n$ into binary sequences in the cube $\{\pm 1\}^m$. When $\mathcal{T}$ consists of well-spread (i.e.,…
Binary embedding of high-dimensional data aims to produce low-dimensional binary codes while preserving discriminative power. State-of-the-art methods often suffer from high computation and storage costs. We present a simple and fast…
Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
We consider the problem of encoding a set of vectors into a minimal number of bits while preserving information on their Euclidean geometry. We show that this task can be accomplished by applying a Johnson-Lindenstrauss embedding and…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
We introduce a novel relaxation of combinatorial discrepancy called Gaussian discrepancy, whereby binary signings are replaced with correlated standard Gaussian random variables. This relaxation effectively reformulates an optimization…
Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for…
3D Gaussian Splatting (3D-GS) has emerged as an efficient 3D representation and a promising foundation for semantic tasks like segmentation. However, existing 3D-GS-based segmentation methods typically rely on high-dimensional category…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
This paper is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly-symmetric stationary…
We study query time bounds for the fundamental problem of estimating the kernel mean $\frac1{|X|}\sum_{x\in X}\mathbf{k}(x,y)$ of a query $y$ in a finite dataset $X\subset\mathbb{R}^d$ up to a prescribed additive error $\varepsilon$. The…
We present here new mechanisms for hashing data via binary embeddings. Contrary to most of the techniques presented before, the embedding matrix of our mechanism is highly structured. That enables us to perform hashing more efficiently and…
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack…
This paper deals with two related problems, namely distance-preserving binary embeddings and quantization for compressed sensing . First, we propose fast methods to replace points from a subset $\mathcal{X} \subset \mathbb{R}^n$, associated…
In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of…
We introduce a novel approach to improve unsupervised hashing. Specifically, we propose a very efficient embedding method: Gaussian Mixture Model embedding (Gemb). The proposed method, using Gaussian Mixture Model, embeds feature vector…